Markov property(Memoryless) P(T≤b+1|7>t)=P(T≤0 Proof P≤1+1> (t<T≤t0+) P(T>to he dt u to+I A(+0)⊥-A(o e he dt (0) e P(T≤D Previous history does not help in predicting the future! Distribution of the time until the next arrival is independent of when the last arrival occurred!Eytan Modiano Slide 7 Markov property (Memoryless) • Previous history does not help in predicting the future! • Distribution of the time until the next arrival is independent of when the last arrival occurred! PT t t T t PT t oof PT t t T t Pt T t t PT t e dt e dt e e e e t t t t t t t t t t t t t t ( | )( ) Pr : ( |) ( ) ( ) | | ( ) ≤+ > = ≤ ≤+ > = <≤+ > = = − − = − + − + − ∞ − + − ∞ − + ∫ ∫ 0 0 0 0 0 0 0 0 0 0 0 0 0 λ 0 λ λ λ λ λ λ − − − =− = ≤ λ λ λ ( ) ( ) ( ) t t t e e PT t 0 0 1